As a method for statistically calculating/displaying a positioning of each observation target (an electronic device or a person) in an overall set, usually, a statistical method such as a principal component analysis, a correspondence analysis, a cluster analysis, a multidimensional scaling method, a self-organization map, a factor analysis and a covariance structure analysis, is used. When each data of the observation target is a frequency distribution set which is non-symmetric and complicated (such as non-normal distribution or multimodal distribution), if the data is not adapted by variable transformation or category classification, it is often difficult that the positioning of each observation target is rationally computed.
On the other hand, from a data set acquired by observing a complicated natural phenomenon or a social phenomenon, a method for extracting new information or a feature pattern and for utilizing them to make clear the phenomenal mechanism, predicate or control, exists. For example, a statistical calculation method such as bootstrap method using Monte Carlo method (by a large number of repeat calculations using a computer) is put to practical use for data mining, as a statistical estimation method.
Many statistical estimation methods are formatted based on mutually independent probability variables Yj with an unknown distribution function F, as a problem to estimate a parameter θ=θ (F) with F. In this case, the parameter θ includes not only a basic statistical quantity such as an average and a moment but also another parameter such as error decision rate of monitoring diagnostics method, a statistical model parameter of a regression model, and a failure probability of reliability prediction. As a feature of the bootstrap method, an estimation quantity is identified by replacing an unknown population distribution F with an empirical distribution Fn (composing a data set). As the empirical distribution, following empirical distribution function is often used.
                    F        n            ⁡              (        y        )              =                  1        n            ⁢                        ∑                      j            =            1                    n                ⁢                  δ          ⁡                      (                                          Y                j                            ≤              y                        )                                ,            -      ∞        <    y    <    ∞  
δ(Yj≦y) is a function defined as follows.
      δ    ⁡          (                        Y          j                ≤        y            )        =      {                            1                                                    Y              j                        ≤            y                                                0                                                    Y              j                        >            y                              
In a conventional technology, in state that data of each observation target is collected with online and an overall set of observation targets is changing in real time, when each positioning in the overall set need be rationally calculated, if scale of a date set acquired from each observation target is large or if the number of observation targets is large, a communication quantity thereof is large and a calculation speed thereof is slow. Furthermore, if data quantity collected is insufficient, proper calculation of a positioning to reflect a true feature of the population distribution F is also difficult. Furthermore, the data quantity to be stored in each observation target and a server becomes large.